Two-step authentication protects email and other accounts from hackers by requiring an extra item of information for a successful login. As well as a username and password, it requires a six-figure code generated on the fly by the app - or else the user has to use one of a prepared list of codes. Each app-generated code can only be used once for a login, and expires after two minutes. The printed list has no time limit, but can only be used once.

A number of people also use the app for other logins - including Dropbox, Dreamhost, Twilio, Evernote and Github - also found that they were locked out of their accounts.

Re-entering details for the accounts is not complex, but can be inconvenient. Some users have suggested other authentication apps, including another iOS app, Authy.

The update introduced support for Apple's "Retina" displays and the iPhone 5, launched last September. The

Google's error in coding for the update points to potential problems with auto-updating of apps, which will be an option introduced in Apple's iOS 7 software, due to be shown off next week when the company is expected to launch new iPhones.

Two-factor authentication is seen as an increasingly important protection against phishing - where hackers use fake sites to capture username and password details - because it blocks a login without the code, which is only available through a mobile phone.

Hacking emails via phishing has been a key avenue for a number of hack attacks recently, most notably by the self-styled Syrian Electronic Army, which used it against a number of media organisations including Associated Press, Reuters, the Guardian, Financial Times, and Washington Post. Two-factor authentication would block such attacks.